Investigation of laminar flow in microtubes with random rough surfaces

Abstract

A new approach of numerically generating a microtube with three-dimensional random surface roughness is presented. In this approach, we combined a bi-cubic Coons patch with Gaussian distributed roughness heights. Two random roughness generation methods are studied. A computational fluid dynamic solver is used to solve the 3-D N–S equations for the flow through the generated rough microtubes with D = 50 μm and L = 100 μm. The effects of the peak roughness height, H, asperities spacing in the θ direction, S θ , and Z direction, S Z , standard deviation of the Gaussian distribution, σ, arithmetical mean roughness, R a, on the Poiseuille number, Po are investigated. It is found that when H/D < 5% the Po number can still be predicted by the conventional flow theory if the mean diameter of rough microtubes, D m, is used to be the hydraulic diameter D h. When H/D = 10%, the main flow is strongly affected by the roughness at Reynolds number Re = 1,500. The Po number increases with Re and deviates from the prediction up to 11.9%. The Po number does not change a lot with S θ and S Z because D m almost keeps constant when the spacing is changed. For the rough microtubes with different R a values, the Po numbers can be almost the same, which prove that only with the R a value we can not determine the friction in the rough microtube. The mean value μ, the maximum and minimum values of the random roughness are found to be critical to determine the Po number.